Results

Bayesian Binomial Test

Bayesian Binomial Test
  Level Counts Total Proportion BF₁₀
. . . . . .
Note.  Proportions tested against value: 0.5. The shape of the prior distribution under the alternative hypothesis is specified by Beta(1, 1).

Inferential Plots

Bayesian Binomial Test: One-sided

Approximately 120 people rated the numbers 0-9 on whether they had a feminine or masculine association with that number.

An early paper by Wilkie and Bodenhausen (2015), claimed that people have a feminine association with even numbers, while having a masculine association with odd numbers. Below are the observed data, based on around 130 (n differs per number) bachelor students.

The Bayesian binomial test gives 2 versions of the Bayes factor and prior posterior plot: one for the proportion of "Feminine" responses, and one for the proportion of "Masculine" responses. In correspondence with the original authors' claims (proportion feminine responses > 0.5 for even numbers; proportion masculine responses > 0.5 for odd numbers), we look at the positive Bayes factor (BF+0) for the even numbers, while looking at the positive Bayes factor for the odd numbers. Note that if we would have done a two-sided test (results provided at the end), the Bayes factor (BF10) will be the same for either proportion (masculine/feminine). For each test, we use uninformed prior distribution(beta (a = b = 1).

Based on the Bayes factors below, I would claim that while there is some evidence for a gendered association for some digits, it is not so simple as stating that odd numbers are feminine and even numbers are masculine. Only for the numbers 1 & 2 did we observe very compelling evidence in favor of the theory. For the numbers 0, 3, 7, 9 we observed some degree of evidence in favor of the null (varying from weak to strong evidence). For 4, 5, 6, and 8 we observed some degree of evidence in favor of the theory (varying from weak to strong evidence).


Bayesian Binomial Test
  Level Counts Total Proportion BF₊₀
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 0 Feminine 59 124 0.476 0.076
  Masculine 65 124 0.524 0.182
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 Feminine 44 128 0.344 0.023
  Masculine 84 128 0.656 120.509
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 Feminine 84 128 0.656 120.509
  Masculine 44 128 0.344 0.023
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 Feminine 63 128 0.492 0.096
  Masculine 65 128 0.508 0.127
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 Feminine 74 126 0.587 1.469
  Masculine 52 126 0.413 0.038
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 Feminine 47 125 0.376 0.029
  Masculine 78 125 0.624 10.474
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 Feminine 79 129 0.612 5.696
  Masculine 50 129 0.388 0.031
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 Feminine 56 127 0.441 0.049
  Masculine 71 127 0.559 0.484
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 Feminine 77 127 0.606 3.864
  Masculine 50 127 0.394 0.032
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 Feminine 74 127 0.583 1.209
  Masculine 53 127 0.417 0.039
Note.  For all tests, the alternative hypothesis specifies that the proportion is greater than 0.5. The shape of the prior distribution under the alternative hypothesis is specified by Beta(1, 1).

An interpretation of the Bayes factors, for each of the 10 digits:

  • 0: the data are 0.076 times as likely under the one-sided alternative hypothesis (which states people have a feminine association with 0), compared to the null hypothesis; this is pretty strong evidence in favor of the null hypothesis. Caveat: zero is a tricky digit, and might be necessarily odd or even.
  • 1: the data are 120 times more likely under the one-sided alternative hypothesis (which states people have a masculine association with 1); this is quite strong evidence for the alternative hypothesis.
  • 2: the data are 120 times as likely under the one-sided alternative hypothesis (which states people have a feminine association with 2); this is quite strong evidence for the alternative hypothesis.
  • 3: the data are 0.127 times as likely under the one-sided alternative hypothesis (which states people have a masculine association with 3); this is moderate evidence for the null hypothesis.
  • 4: the data are 1.47 times as likely under the one-sided alternative hypothesis (which states people have a feminine association with 4); this is weak evidence for the alternative hypothesis.
  • 5: the data are 10.5 times as likely under the one-sided alternative hypothesis (which states people have a masculine association with 5); this is pretty strong evidence for the alternative hypothesis.
  • 6: the data are 5.7 times as likely under the one-sided alternative hypothesis (which states people have a feminine association with 6); this is moderate evidence for the alternative hypothesis.
  • 7: the data are 0.48 times as likely under the one-sided alternative hypothesis (which states people have a masculine association with 7); this is weak evidence in favor of the null hypothesis.
  • 8: the data are 3.9 times as likely under the one-sided alternative hypothesis (which states people have a feminine association with 8); this is moderate evidence in favor of the alternative hypothesis.
  • 9: the data are 0.039 times as likely under the one-sided alternative hypothesis (which states people have a masculine association with 9); this is strong evidence against the null hypothesis


Inferential Plots

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 0 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 0 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 - Masculine

Prior and Posterior


S.S. Bayesian Correlation

Bayesian Correlation Table
n r BF₁₀ p
30 0.400 1.079 0.029

Inferential Plots

Prior and Posterior

Bayesian Binomial Test: Two-sided

Bayesian Binomial Test
  Level Counts Total Proportion BF₁₀
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 Feminine 44 128 0.344 60.266
  Masculine 84 128 0.656 60.266
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 Feminine 84 128 0.656 60.266
  Masculine 44 128 0.344 60.266
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 Feminine 63 128 0.492 0.112
  Masculine 65 128 0.508 0.112
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 Feminine 74 126 0.587 0.753
  Masculine 52 126 0.413 0.753
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 Feminine 47 125 0.376 5.251
  Masculine 78 125 0.624 5.251
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 Feminine 79 129 0.612 2.863
  Masculine 50 129 0.388 2.863
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 Feminine 56 127 0.441 0.267
  Masculine 71 127 0.559 0.267
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 Feminine 77 127 0.606 1.948
  Masculine 50 127 0.394 1.948
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 Feminine 74 127 0.583 0.624
  Masculine 53 127 0.417 0.624
Note.  Proportions tested against value: 0.5. The shape of the prior distribution under the alternative hypothesis is specified by Beta(1, 1).

Inferential Plots

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 - Masculine

Prior and Posterior

Bayesian Binomial Test: Two-sided

Approximately 120 people rated the numbers 0-9 on whether they had a feminine or masculine association with that number.

An early paper by Wilkie and Bodenhausen (2015), claimed that people have a feminine association with even numbers, while having a masculine association with odd numbers. Below are the observed data, based on around 130 (n differs per number) bachelor students.

The Bayesian binomial test gives 2 versions of the Bayes factor and prior posterior plot: one for the proportion of "Feminine" responses, and one for the proportion of "Masculine" responses. In correspondence with the original authors' claims (proportion feminine responses > 0.5 for even numbers; proportion masculine responses > 0.5 for odd numbers), we look at the positive Bayes factor (BF+0) for the even numbers, while looking at the positive Bayes factor for the odd numbers.

Based on the Bayes factors below, I would claim that while there is some evidence for a gendered association for some digits, it is not so simple as stating that odd numbers are feminine and even numbers are masculine. Only for the numbers 1 & 2 did we observe very compelling evidence in favor of the theory. For the numbers 0, 3, 7, 9 we observed some degree of evidence in favor of the null (varying from weak to strong evidence). For 4, 5, 6, and 8 we observed some degree of evidence in favor of the theory (varying from weak to strong evidence).


Bayesian Binomial Test
  Level Counts Total Proportion BF₁₀
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 0 Feminine 59 124 0.476 0.129
  Masculine 65 124 0.524 0.129
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 Feminine 44 128 0.344 60.266
  Masculine 84 128 0.656 60.266
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 Feminine 84 128 0.656 60.266
  Masculine 44 128 0.344 60.266
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 Feminine 63 128 0.492 0.112
  Masculine 65 128 0.508 0.112
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 Feminine 74 126 0.587 0.753
  Masculine 52 126 0.413 0.753
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 Feminine 47 125 0.376 5.251
  Masculine 78 125 0.624 5.251
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 Feminine 79 129 0.612 2.863
  Masculine 50 129 0.388 2.863
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 Feminine 56 127 0.441 0.267
  Masculine 71 127 0.559 0.267
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 Feminine 77 127 0.606 1.948
  Masculine 50 127 0.394 1.948
Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 Feminine 74 127 0.583 0.624
  Masculine 53 127 0.417 0.624
Note.  Proportions tested against value: 0.5. The shape of the prior distribution under the alternative hypothesis is specified by Beta(1, 1).

An interpretation of the Bayes factors, for each of the 10 digits:

  • 0: the data are 0.076 times as likely under the one-sided alternative hypothesis (which states people have a feminine association with 0), compared to the null hypothesis; this is pretty strong evidence in favor of the null hypothesis. Caveat: zero is a tricky digit, and might be necessarily odd or even.
  • 1: the data are 120 times more likely under the one-sided alternative hypothesis (which states people have a masculine association with 1); this is quite strong evidence for the alternative hypothesis.
  • 2: the data are 120 times as likely under the one-sided alternative hypothesis (which states people have a feminine association with 2); this is quite strong evidence for the alternative hypothesis.
  • 3: the data are 0.127 times as likely under the one-sided alternative hypothesis (which states people have a masculine association with 3); this is moderate evidence for the null hypothesis.
  • 4: the data are 1.47 times as likely under the one-sided alternative hypothesis (which states people have a feminine association with 4); this is weak evidence for the alternative hypothesis.
  • 5: the data are 10.5 times as likely under the one-sided alternative hypothesis (which states people have a masculine association with 5); this is pretty strong evidence for the alternative hypothesis.
  • 6: the data are 5.7 times as likely under the one-sided alternative hypothesis (which states people have a feminine association with 6); this is moderate evidence for the alternative hypothesis.
  • 7: the data are 0.48 times as likely under the one-sided alternative hypothesis (which states people have a masculine association with 7); this is weak evidence in favor of the null hypothesis.
  • 8: the data are 3.9 times as likely under the one-sided alternative hypothesis (which states people have a feminine association with 8); this is moderate evidence in favor of the alternative hypothesis.
  • 9: the data are 0.039 times as likely under the one-sided alternative hypothesis (which states people have a masculine association with 9); this is strong evidence against the null hypothesis


Inferential Plots

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 0 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 0 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 - Masculine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 - Feminine

Prior and Posterior

Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 - Masculine

Prior and Posterior